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Stability and Asynchronous Stabilization for a Class of Discrete-time Switched Nonlinear Systems with Stable and Unstable Subsystems

Qunxian Zheng*, Hongbin Zhang, and Dianhao Zheng
International Journal of Control, Automation, and Systems, vol. 15, no. 3, pp.986-994, 2017

Abstract : "The stability analysis and asynchronous stabilization problems for a class of discrete-time switched nonlinear systems with stable and unstable subsystems are investigated in this paper. The Takagi-Sugeno (T-S) fuzzy model is used to represent each nonlinear subsystem. Through using the T-S fuzzy model, the studied systems are modeled into the switched T-S fuzzy systems. By using the switching fuzzy-basis-dependent Lyapunov functions (FLFs) approach and mode-dependent average dwell time (MDADT) technique, the stability conditions for the open-loop switched T-S fuzzy systems with unstable subsystems and asynchronous stabilization conditions for the closed-loop switched T-S fuzzy systems with unstable subsystems are obtained. Both the stability results and asynchronous stabilization results are derived in terms of linear matrix inequalities (LMIs). Finally two numerical examples are provided to illustrate the effectiveness of the results obtained."

Keyword : Discrete-time switched nonlinear systems, mode-dependent average dwell time, switching fuzzy-basisdependent Lyapunov functions, Takagi-Sugeno fuzzy model, unstable subsystems.

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